Large Eddy Simulation in Aid of RANS Large Eddy Simulation in Aid of RANS Modelling Modelling M A Leschziner Imperial College London RANS/LES simulation of flow around a highly- swept wing NUS Turbulence NUS Turbulence Workshop, Aug. ‘04 Workshop, Aug. ‘04
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Large Eddy Simulation in Aid of RANS Modelling M A Leschziner Imperial College London RANS/LES simulation of flow around a highly-swept wing NUS Turbulence.
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Large Eddy Simulation in Aid of RANS ModellingLarge Eddy Simulation in Aid of RANS Modelling
M A Leschziner
Imperial College London
RANS/LES simulation of flow around a highly-swept wing
NUS Turbulence NUS Turbulence Workshop, Aug. ‘04Workshop, Aug. ‘04
CollaboratorsCollaborators
Lionel Temmerman
Anne Dejoan
Sylvain Lardeau
Chen Wang
Ning Li
Fabrizio Tessicini
Yong-Jun Jang
Ken-ichi Abe
Kemo Hanjalic
RANS may be something of a ‘can of worms’, but is here to stay
Decisive advantages:
Economy, especially in
statistical homogeneous 2d flows
when turbulence is dominated by small, less energetic scales
in the absence of periodic instabilities
Good performance in thin shear and mildly-separated flows, especially
near walls
Predictive capabilities depend greatly on
appropriateness of closure type and details relative to flow characteristics
quality of boundary conditions
user competence
The Case for RANSThe Case for RANS
Challenges to RANSChallenges to RANS
Dynamics of large-scale unsteadiness and associated non-locality
Massive separation – large energetic vortices
Unsteady separation from curved surfaces
Reattachment (always highly unsteady)
Unsteady instabilities and interaction with turbulence
Strong non-equilibrium conditions
Interaction between disparate flow regions
post reattachment recovery
wall-shear / free-shear layers
Highly 3d straining – skewing, strong streamwise vorticity
Separation from Curved Surfaces - Tall Order for RANS?Separation from Curved Surfaces - Tall Order for RANS?
0 1 2 3 4 5 6 7 8 90
1
2
3
AL model with k - equation(Separation : X/H = 0.26, Reattachment : X/H = 4.7)Y/H
X/H
Reverse flow
LES instantaneous realisations
RANS
Dynamics of Separated FlowDynamics of Separated Flow
Steady
Unsteady
Separation
Dynamics of Separated FlowDynamics of Separated Flow
Steady Reattachment
Recovery
Attached
RANS DevelopmentsRANS Developments
Desire to extent generality drives RANS research
Non-linear eddy-viscosity models
Explicit algebraic Reynolds-stress models
Full second-moment closure
Structure-tensor models
multi-scale models…
Simulation plays important role in aiding development and validation
Traditionally, DNS for homogeneous and channel flow at low Re used
Increasingly, LES exploited for complex flow
2 ; { , , }; { , , }
3ji
i j t ij i ii i
UUu u k U U V W x x y z
x x
2 2 2 2
3u v w k
Channel flow
2u
2v
Which is wrong
Generalised eddy-viscosity hypothesis:
Wrongly implies that eigenvalues of stress and strain tensors aligned
Wrong even in thin-shear flow:
The Argument for Resolving AnisotropyThe Argument for Resolving Anisotropy
The Argument for Resolving AnisotropyThe Argument for Resolving Anisotropy
LES can play a very useful role in support of RANS modelling elucidating physics providing wealth of data for validation and a-priori study of closure proposals, especially budget
Necessarily a very costly approach, because of resolution demands
can only be done at relatively low Re
Hybrid RANS / LES strategies hold some promise, but difficult
very active area of research
Concluding RemarksConcluding Remarks
NUS Turbulence NUS Turbulence Workshop, Aug. ‘04Workshop, Aug. ‘04
Near-Wall Modelling in LESNear-Wall Modelling in LES
M.A. Leschziner
Imperial College London
Hybrid RANS-LESHybrid RANS-LES
Wall resolved LES is untenable in high-Re near-wall flow
Near-wall treatment is key to utility of LES in practice
Several approaches:
Wall functions
Zonal methods – thin-shear-flow equations near wall
Hybrid RANS-LES (+ synthetic turbulence)
All pose difficult fundamental and practical questions:
Compatibility of averaging with filtering
Applicability of RANS closure – time-scale separation
Interface conditions
LES / Wall-FunctionsLES / Wall-Functions
Channel flow, Re=12000, 96x64x64 grid
LES / Wall-FunctionsLES / Wall-Functions
2d hill flow, Re=2.2x104, 0.6M nodes
LES / Wall-FunctionsLES / Wall-Functions
Hydrofoil trailing edge, Re=2x106, 384x64x24 grid
Hybrid RANS-LESHybrid RANS-LES
Methodology
Target
Velocity
Turbulent viscosity
Turbulence energy
SuperimposedRANS layer
Interface conditions
LESRANS UU intint LESt
RANSt int,int,
LESRANS kk intmod,intmod,
Hybrid RANS-LESHybrid RANS-LES
Implementation
mod modRANS LES
0.5 2mod mod or / RANS RANSC l k C k
mod,int,int 0.5
,int
LES
RANS
Cl k
< . > : spatial average in the homogeneous directions.
,int
int int
1 exp( ) 0.09 0.09
1 exp
yC y C
y
Alternative: instantaneous value
Hybrid RANS-LESHybrid RANS-LES
Typical variation of mean in channel flow , 1-eq. RANS model
C
at interface across RANS layer
Hybrid RANS-LESHybrid RANS-LES
Variations of mean and instantaneous in channel flow, 1-eq. RANS model
C
Hybrid RANS-LESHybrid RANS-LES
512 128 128
326464
Channel flow, Re=42200
17 - 135int jy
Hybrid RANS-LESHybrid RANS-LES
Channel flow, Re=42200
Resolved
Modelled
DES
Hybrid RANS-LESHybrid RANS-LES
Channel flow, Re=42200, velocity and shear stress distributions for two interface positions
Hybrid RANS-LESHybrid RANS-LES
Variations of mean and instantaneous in channel flow, 2-eq.
RANS model, Re=2000
C
Hybrid RANS-LESHybrid RANS-LES
Velocity in channel flow, 2-eq. RANS model, Re=2000, average and instantaneous input of C
Hybrid RANS-LESHybrid RANS-LES
Structure (streamwise vorticity) in channel flow, 2-eq. RANS
model, Re=2000
Interface y+=610Interface y+=120
Hybrid RANS-LESHybrid RANS-LES
2d-hill flow, Re=21500, interface conditions
Grid: 112x64x56=4x105
against reference of 4.6x106
Hybrid RANS-LESHybrid RANS-LES
2d-hill flow, Re=21500, variations of C
Hybrid RANS-LESHybrid RANS-LES
2d-hill flow, Re=21500, variations of velocity and shear stress
Hybrid RANS-LESHybrid RANS-LES
2d-hill flow, Re=21500, variations of velocity and shear stress
Hybrid RANS-LESHybrid RANS-LES
2d-hill flow, Re=21500, variations of velocity against log-law
Hybrid RANS-LESHybrid RANS-LES
2d-hill flow, Re=21500, variations of turbulent viscosity
Low-Re solution
In sublayer
Two-Layer ModelTwo-Layer Model
Methodology
Near-wall control volume divided into subgrid volumes
Transport equations solve across the subgrid for:
Mean-flow parameters: U, W
Wall-normal V-velocity from continuity within subgrid
Two-Layer ModelTwo-Layer Model
Methodology
Wall-parallel pressure gradient (dP/dx) calculated from main-grid and assumed constant across subgrid
calculated from subgrid solution
wall ,kP
applied to main-grid as in standard wall-function treatments
wall
y
U
ydx
dP
y
UV
x
UU t
Two-Layer ModelTwo-Layer Model
Methodology
Similar to 1-D convection-diffusion problem
Finite-volume method
Central differences for diffusion and for convection
Tri-diagonal matrix algorithm
Average solution in time
No need to solve Poisson equation
Very fast!
Desider: 6 month meeting
Numerical solution in sublayer
Two-Layer ModelTwo-Layer Model
pressureStreamwise velocity
Two-Layer ModelTwo-Layer Model
Trailing-edge separation from hydrofoil; Re=2.2x106
512x128x24 nodesComparison with highly-resolved LES by Wang, 1536x96x48 nodes Sub-layer thickness
40y
Two-Layer ModelTwo-Layer Model
Streamwise-velocity contours
Wall model
B C D E F G
X/h
|U|/U_e
Full LESWall model (dynamic SGS)
Two-Layer ModelTwo-Layer Model
Velocity magnitude
Two-Layer ModelTwo-Layer Model
Full LESWall model (dynamic SGS)
Turbulence energy
Full LESWall model (dynamic SGS)
Two-Layer ModelTwo-Layer Model
Streamwise velocity in wake
Full LESWall model (dynamic SGS)
Two-Layer ModelTwo-Layer Model
Skin friction
Concluding RemarksConcluding Remarks
The jury is out on the prospect of approximate wall modelling as a general approach
There is evidence that some offer ‘credible’ solutions and gains in economy
There is a price to pay (sometimes high) in terms of physical realism (e.g. near-wall structure)
Particular problem: loss of small-scale near-wall components
It is not clear what to do in very complex near-wall flow – separation, severe 3d straining
Particular problems when near-wall flow has a strong effect on global flow features
Hybrid RANS-LES and zonal modelling work, but much more research is required to identify applicability and limitations